A single-particle framework for unitary lattice gauge theory in discrete time
Quantum Physics
2025-12-09 v4 Other Condensed Matter
High Energy Physics - Lattice
Abstract
We construct a real-time lattice-gauge-theory-type action for a spin-1/2 matter field of a single particle on a (1+1)-dimensional spacetime lattice. The framework is based on a discrete-time quantum walk, and is hence inherently unitary and strictly local, i.e., transition amplitudes exactly vanish outside of a lightcone on the lattice. We then provide a lattice Noether's theorem for internal symmetries of this action. We further couple this action to an electromagnetic field by a minimal substitution on the lattice. Finally, we suggest a real-time lattice-gauge-theory-type action for the electromagnetic field in arbitrary spacetime dimensions, and derive its classical equations of motion, which are lattice versions of Maxwell's equations.
Keywords
Cite
@article{arxiv.2208.14997,
title = {A single-particle framework for unitary lattice gauge theory in discrete time},
author = {Pablo Arnault and Christopher Cedzich},
journal= {arXiv preprint arXiv:2208.14997},
year = {2025}
}